A118412 Denominator of sum of reciprocals of first n pentatope numbers A000332.

1, 5, 15, 105, 42, 63, 90, 495, 55, 143, 91, 1365, 420, 510, 612, 2907, 855, 665, 385, 1771, 1518, 1725, 1950, 8775, 2457, 5481, 1015, 4495, 1240, 4092, 4488, 19635, 5355, 11655, 6327, 9139, 2470, 2665, 8610, 37023, 9933, 21285, 11385, 48645, 4324, 4606, 4900

Offset

1,2

Comments

Numerators are A118411. The denominator of sum of reciprocals of first n triangular numbers is A026741. The denominator of sum of reciprocals of first n tetrahedral numbers is A118392.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

A118411(n)/A118412(n) = Sum_{i=1..n} 1/A000332(i+3).

A118411(n)/A118412(n) = Sum_{i=1..n} 1/C(i+3,4).

A118411(n)/A118412(n) = Sum_{i=1..n} 24/(i*(i+1)*(i+2)*(i+3)).

Example

a(1) = 1 = denominator of 1/1.
a(2) = 5 = denominator of 6/5 = 1/1 + 1/5.
a(3) = 15 = denominator of 19/15 = 1/1 + 1/5 + 1/15.
a(4) = 105 = denominator of 136/105 = 1/1 + 1/5 + 1/15 + 1/35.
a(5) = 42 = denominator of 55/42 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70.
a(10) = 143 = denominator of 190/143 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70 + 1/126 + 1/210 + 1/330 + 1/495 + 1/715.
a(20) = 1771 = denominator of 2360/1771 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70 + 1/126 + 1/210 + 1/330 + 1/495 + 1/715 + 1/1001 + 1/1365 + 1/1820 + 1/2380 + 1/3060 + 1/3876 + 1/4845 + 1/5985 + 1/7315 + 1/8855.

Mathematica

Denominator[Accumulate[1/Binomial[Range[4, 50], 4]]] (* Paolo Xausa, Sep 27 2025 *)

Prog

(PARI) s=0; for(i=4, 50, s+=1/binomial(i, 4); print1(denominator(s)", ")) /* Phil Carmody, Mar 27 2012 */

Crossrefs

Cf. A000332, A022998, A026741, A118391, A118391, A118411.

Sequence in context: A268565 A358197 A121869 * A068622 A080449 A088418

Adjacent sequences: A118409 A118410 A118411 * A118413 A118414 A118415

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Apr 27 2006

Extensions

More terms from Jason Yuen, Sep 27 2025

Status

approved